Bitcoin Forum

I just created this wiki page (https://en.bitcoin.it/wiki/Two-factor_paper_wallet).

I'm coining the term here, I think ... not sure what was it called when discussed on Bitcointalk.

My question is: Has anyone implemented this "2 factor paper wallet"? Is it being worked on?

x-post to SE (http://bitcoin.stackexchange.com/questions/4337/is-anyone-working-on-has-implemented-a-two-factor-paper-wallet)

How about a 2-of-2 multisig address? I believe it's in development now.

https://en.bitcoin.it/wiki/BIP_0011
https://en.bitcoin.it/wiki/BIP_0019

This is Similar.

This proposal doesn't require any protocol change, or in fact any changes to Bitcoin code.
It's just an external service that can be implemented today without much effort.

https://en.bitcoin.it/wiki/User:Casascius/Base58Check-encoded_objects_proposal

It's no harder to generate the initial pair yourself as it is to validate that it is correct. If you don't validate it, and it turns out to be defective in any way, your money is forever lost.

Frankly, this seems silly to me. What advantage do you get from splitting the key in this way?

Impeccable timing... I just created this wiki page (https://en.bitcoin.it/wiki/User:Casascius/Base58Check-encoded_objects_proposal) that takes a stab at addressing the very thing you've asked about.

1 - the ability to put your key in 2 different geographically separate places to protect them from snooping/theft.  example, I might put one half in my safety deposit box and keep the other half at home, so someone from the bank who happens to gain access to my safety deposit box doesn't get my bitcoins.

2 - the ability to have 2 separate machines generate a single key, so even if one or both machines is compromised, the resulting key is not.  (Example: Smartphone + Computer). All that matters is that both machines aren't compromised by the same person or someone with the ability to access both halves.

That can be done much simpler ways. For example, you can literally separate the key bits in half. You can also generate a random sequence the same length as the key, and store that along with the key XORed with that.

Any scheme that doesn't involve storing the private key on a single device has this property.

Agreed, simpler for the computer.  (though separating the key bits in half definitely works, is simple for the user, and I've done it).

By writing the proposal, I'm hoping it leads to something simple for the user.

Ultimately, the user should just be able to click a button, and get however many codes he wants.  I will probably update my Casascius Bitcoin Utility to generate all of these codes, as well as turn them back into a single standard private key for import.



No single device can generate a single key without storing it in memory, at least temporarily.  And it has to send the key somewhere through some sort of i/o for it to be of any use.  Interception is possible at either point by malware that knows what it's looking for.  Bottom line, I think most would agree that a wallet generator being immune to an unknown compromise is a desirable feature if it is not too complicated or inconvenient to use.

Using EC multiplication rather than XOR has the convenient property that machine 1 can share what it needs with machine 2 in the form of an EC point (like a public key), and neither machine will ever be able to know the complete final private key until the user redeems the wallet.

For the private key splitting, your approach of storing parts combined with a global XOR seems to be redundant against only one failure. But why not expand the concept to an arbitrary (n,k)-redundant encoding? Here's a quick brainstorm of how a scheme might work:

1. Take your private key and find n values (which we'll call v(1) to v(n)) which meet the following conditions:

i. v(k) <= 2 ^ 256 / (k)^(3*n)
ii. hex(SHA256(k)) starts with '00' - this is the checksum
iii. XOR(v(k) for all k 1 to n) = the original private key

The first condition isn't too important, it's just nice to have if you want all of your pieces to stay within 64 bytes.

Now, for the pieces. Piece k will have the following format (encoded into base 58 of course):

Byte 0 = 0x86 (or whatever)
Byte 1 = k
Byte 2 = string length of the resulting base58
Bytes 3-whatever = v(1) + v(2)*2^k + v(3)*3^k + v(4)*4^k + ...

For example, if you want your private key to require three out of five pieces to reconstitute, the final pieces will be (string lengths will depend on exactly what v(1), v(2) and v(3) are):

0x86 1 45 v(1) + v(2)*2 + v(3)*3
0x86 2 45 v(1) + v(2)*4 + v(3)*9
0x86 3 46 v(1) + v(2)*8 + v(3)*27
0x86 4 46 v(1) + v(2)*16 + v(3)*81
0x86 5 46 v(1) + v(2)*32 + v(3)*243

To reconstitute the private key, simply solve the linear system from any three pieces and XOR all the results. You actually don't have to know what n is because you can simply assume that n is the number of pieces that you have, and if you have too many pieces solving the linear system will simply lead you to discover that the n+1st, n+2nd, etc pieces are all equal to zero.

The scheme can easily be adapted to make the private key the EC product of v(1), v(2), etc rather than an XOR, and even the linear systems can be changed to an multiplicative/exponential equivalent if desired, so it's pretty adaptable.

If "why not" is a question, the honest answer is because I don't understand the math well enough to propose such a thing, though I agree that an encoding that allows redundancy against an arbitrary number of failures is more desirable than a scheme that allows redundancy against only one, except perhaps if implementing the scheme is too difficult for developers that they just don't do it.  (Your suggestion on its surface appears to not have this problem).

If "why not" is a suggestion, well then, hell yeah!

Would you be willing to write your suggestion up on the wiki and assume that your reader doesn't understand the math?  For example, when you say "find n values that meet the following conditions", it's not obvious to me how one would go about finding such a value.

Watching!

It is actually supported by the protocol now. I talked about it in this thread: https://bitcointalk.org/index.php?topic=94723.msg1047595#msg1047595 (https://bitcointalk.org/index.php?topic=94723.msg1047595#msg1047595)

https://en.bitcoin.it/wiki/User:Vbuterin/K_of_N_redundant_offline_private_key_proposal

Fairly technical (hard to avoid that when describing these types of protocols), but here you go.

Good news!  I got some code working that generates these for any k,n up to 7.

I meant to make it up to 8, but I overflow the amount of space I've given myself when doing an 8 of 8 scheme, so will need to tweak it for that bit to fit. But 7 of 8 won't overflow.

The code totally works!... generating a random key and bitcoin address in n parts, and is able to recreate it with k strings.  I modified your proposal a little bit, and then wrote my code to be consistent with it.

Sample!  Any 7 of the following 8... (as indicated by prefix 6s7, the 7 means how many is needed):
6s755BvvkPDD6VpEZVB8vMbDPDGZSVdEX4BCPGmEdXp1NifbBQ7ALFGnmTN
6s75WdT4MPbeYr43nDjFpq944VqRRJJdNKd1Zv9GioScjbt8tUeBjn1fUzN
6s75x4yCDj15iukjhH51Td9hJWdXzqVtExFVAVkHwfhHWsqGwUyGhvxyhbG
6s76PWVMkSrWktWADeHJDTL743zPbkbXTYNxtWUYbARVVYpTABTr2JwCo88
6s76px1hvUvTZwfzgF2eZb4BcM2pQCzuKjAvAnsf34T6hvtAhq4BGgmWgtn
6s77GPZFG2Twgj1auFPMKYzr4mzckXT4YG5GMZPwqZyjkfqfHGNGnCmuEsf
6s77hqEdScKDWpgZM7u158kSE4L4kxYFRDHXrQZQ7R1dautwg7WugaNruau
6s789Hp6fCk35xAaKpC9qnFdLD2fZjQx6YQ2RYgX4zTnPxYiexY1yfoHCym

Yields the following bitcoin private key and bitcoin address with my test app.  I'm using XOR to combine v(1) thru v(7) once calculated.
5KGysrJEuNxE6aZKytbRi9CYTzPefGBrVEG7cWXrnzXq7jte48B
13AKe4Ha5XAWWsQWwFqM2EwXiPHjJM2t6v

Any 3 of the following 5
6s3CKaXLZf36aRuAprra2RmEG94pQdD2hYWyevKzdkVvZ1DWvY9qAVtmPSo
6s3Cm23U7kL2Rtod4uTYPUMfLq5akewRNhEbPxhUfWDFiuLtMrnWzFuP3qb
6s3DCTZbfzgPzM8FrutYZCwJwjLkrEPfQD1k723bx8Wh1BWLyGBji26PK3G
6s3Ddu5jEf2mGR2BxtGzdgbg5Wp2u9XqfJpM7beyNwLuRbu9vwTTB2313sc
6s3E5LbrpT2StcHXJuUVRjkKkSqNDUnazAP1qgihyRJNtTEBbVUSz9ajDJS

yields this private key and address.
5KELsahJpMfwu7fvMfSMm7rnG5voCTE4P9D6ikR7L6ajeQgpj7U
1PWYZB7kLLjm8Ue3pvAEeHMBJr6KXgdR6K

Math isn't my strong suit. Let me get this straight:
m-of-n is when m=n-1
K-of-N is when k=n-2

m-of-n and k-of-n are the same... differing only by a letter which was arbitrarily chosen. the only difference is the first proposal I wrote required that m be n-1 (the letters themselves don't matter)... the proposal that Vitalik wrote (which I coded and seems to work) allows m to be as low as 1 and as much as n.  If you substitute k for n, everything is the same, you have merely changed the letter.

simple and freaking ingenious, Im sold :)

edit: pull out a pair of scissors ffs and problem solved :P

With a scheme like this, is it possible to create an interdependence of keys where a community has keys that overlap within and between groups? For instance, an apartment building where everyone needs keys from their next door neighbors with 3 of 5 so either side or two on the same side will do. This would create an interdependent web. If this works, it would make for some interesting banking schemes.

OK, I have baked the M-of-N wallet code into my Casascius Bitcoin Utility, just as a proof of concept.  The M-of-N calc is under "Tools".

Source and binaries are included in this ZIP file.  This is for Windows.

https://www.casascius.com/BtcAddressMN.zip

This won't yet print any M-of-N paper wallets - it will simply produce the M-of-N codes (which you can copy and paste away), and recombine any M of them back into a regular private key (if you copy and paste them back in).  It could probably use a lot of scrutiny and testing, but it seems to work like it should.

Nice!

I'll come up with a cross-platform python utility for this when I have time.

I did not know this was possible. A utility like this combined with with user created m-of-n keys by nesting could create a system where a quorum of individuals could unlock certain amounts of funds depending on how many keys are used. I'm tripping over this.

Now that I have it working, I am thinking of how it could evolve a bit:

for example, solving m-of-n yields 1 bitcoin address.  But practical use of the scheme might be an "in-case-I-die" safety measure, and I am thinking the keys ought to contain a field to say how many addresses are intended to be used (using the sum as a deterministic wallet seed).

For example if I am going to go to the effort of passing out around key parts, it's going to be a real pain in the ass each time I need to discard the address I'm using, so it would be better if when my loved ones went to restore my coins, the restore utility would know, "aha! this yields 24 addresses" and prints out 3 pages of paper wallets with 8 addresses per page.

The output from several randomly generated k-of-n keys could be the inputs of user defined m-of-n transactions.

You could use a key family scheme to generate as many addresses as you want from a single seed - something like this:

http://crypto.stackexchange.com/questions/1534/families-of-public-private-keys-in-elliptic-curve-cryptography

It also has the advantage that you could store some derivative privkeys in a more accessible place (eg. desktop client, blockchain.info) and use them normally without risking your root key being compromised.

These m-of-n transactions (when nested) are starting to look like discrete components and Bitcoin is the energy. Combining different types of transactions could create logic gates of money. The circuit would be traceable by the blockchain, though it would create a lot of transactions. That's something to worry about later. I'm thinking that this could be a way to create community based lending systems that amplify funds for borrowers that meet the criteria of key persons in the circuit. There would be many different functions for different amounts depending on the setup, enough to meet the needs of borrowers of all sorts. Thoughts, or should I just start drinking?

Hello,
Maybe relevant:

I'm working on a "traditional" two factor wallet, called SmartCardWallet. In essence you shall have a physical card in your wallet, that acts something like a normal chipped visa card. Unlike paper based solutions, it is considered a difficult task for an average adversary to copy/attack the contents of a smart card. See https://bitcointalk.org/index.php?topic=94119.0

When I read halfway down the first page I realised it was exactly what I needed. I've been thinking about the idea of having a private key to some GPG encrypted information stored in such a way that you only need say 3/5 keys to decrypt the information. That way, you can communicate from inside an absolutely sealed environment and save things like passwords or details of assets and projects and particularly bitcoins, and save all that information with a measure of security but entirely outside of your control. By holding on to one of the keys yourself, perhaps a crucial key, you could ensure nothing could happen while you were alive. I want to experiment with a 2-tiered system, as in you need [3/5 root keys], or [2/5 root and ANY 3 of like 8 secondary keys]; that is that the secondary keys are not particular to the lost root keys.

Anyway, don't mind me.

Subbed.

Is this the same math as Shamir Secret Sharing (http://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing) (using polynomials) or something different? I've used that before to encode my password safe in several places and I'm sure it would work easily for keys too.

Sure, all you need to do for that is to set up a (3,6) system where one of the six outputs is itself stored in the form of a (3,8) system.

So, here's my current version of the Python utility:

https://www.dropbox.com/sh/ysbyb3v5zec43pe/Emrn5v2slX/files.zip

The one thing I can't figure out is what it exactly means to take the "SHA256(resulting bitcoin address)". Do I SHA256 the address itself? A bytestring version of it? A bytestring version padded with '\x00'? None of those seems to work. But barring that my utility is decoding Casascius's example correctly.

Another question/concern: why limit it to (8,8)? There is no need whatsoever to do this. All you have to do is keep applying progressively smaller caps to the high-position intermediate k-values and as long as the cap keeps decreasing fast enough there's no problem - I implemented it in my code already. We can limit it to (16,16) and have 8 bytes of error correction in the encoding instead of 9 and everything will work just fine.

Does this mean if either part is lost, you lose access to any coins in there?

If you have a 1-of-2 split, then either part is fine to get you the key.
If you have a 4-of-5 split, then if any two of the five parts are lost you lose access to the key.
If you have a 8-of-11 split, then if any four of the eleven parts are lost you lose access to the key.

Also, there's a new thread now: https://bitcointalk.org/index.php?topic=104086.msg1139496#msg1139496

I think you mean "any four of the eleven".

Indeed. Fixed.